1. Field of the Invention
The present invention concerns magnetic resonance tomography (MRT) in general, as applied in medicine to examine patients. The present invention concerns a method as well as an MRT system to implement the method that significantly reduce the computation time in PPA-based image reconstruction according to known PPA methods (for example GRAPPA) without loss of signal-to-noise ratio (SNR).
2. Description of the Prior Art
MRT is based on the physical phenomenon of nuclear magnetic resonance and has been successfully used for over 15 years as an imaging modality in medicine and biophysics. In this examination modality, the subject is exposed to a strong, constant magnetic field. The nuclear spins of the atoms in the subject, which were previously randomly oriented, thereby align.
Radio-frequency energy can now excite these “ordered” nuclear spins to a specific oscillation. This oscillation generates the actual measurement signal in MRT, which measurement signal is acquired by means of suitable acquisition coils. The measurement subject can thereby be spatially coded in all three spatial directions by the use of non-homogeneous magnetic fields generated by gradient coils. This allows a free selection of the slice to be imaged, so slice images of the human body can be acquired in all directions. As a non-invasive examination method, MRT as a slice imaging method in medical diagnostics is primarily characterized by a versatile contrast capability. Due to the excellent presentation capability of the soft tissue, MRT has developed into a method superior in many ways to x-ray computed tomography (CT). MRT today is based on the application of spin echo and gradient echo sequences that enable an excellent image quality with measurement times on the order of seconds to minutes.
The steady technical development of the components of MRT apparatuses and the introduction of fast imaging sequences continues to open more fields of use for MRT in medicine. Real-time imaging to assist minimally-invasive surgery, functional imaging in neurology and performance measurement in cardiology are only a few examples. In spite of the technical advances in the construction of MRT apparatuses, acquisition times and signal-to-noise ratio (SNR) of an MRT image remain limiting factors for many applications of MRT in medical diagnostics.
A reduction of the acquisition time (the data acquisition time) while maintaining an acceptable SNR is desirable, particularly in functional imaging in which a significant movement of the subject or parts of the subject is always present (blood flow, heart movement, peristalsis of the abdomen etc.). In general, movement causes artifacts in an MRT image, for example movement artifacts that increase with the duration of the data acquisition time. In order to improve the image quality, it would be conceivable to acquire multiple images and to later superimpose these images. This does not always lead to an intended improvement of the overall image quality, however, particularly with regard to the movement artifacts. For example, the SNR is improved while the movement artifacts increase.
One approach to shorten the measurement time and thereby to keep the SNR loss within acceptable limits is to reduce the quantity of the image data to be acquired. In order to obtain a complete image from such a reduced data set, either the missing data must be reconstructed with suitable algorithms or the incomplete image must be corrected from the reduced data. The acquisition of the data in MRT occurs in a mathematical configuration known as k-space (local frequency domain). The MRT image in image space (image domain) is linked with the MRT data in k-space by means of Fourier transformation. The spatial coding of the subject which spans k-space occurs by means of gradients in all three spatial directions. In the case of 2D imaging, the slice selection (establishes an acquisition slice in the subject, typically the z-axis), the frequency coding (establishes a direction in the slice, typically the x-axis) and the phase coding (determines the second dimension within the slice, typically the y-axis) are thereby differentiated. In the case of 3D imaging, the slice selection is replaced by a second phase coding direction. Without limitation as to generality, in the further course of the description herein a two-dimensional Cartesian k-space is assumed that is scanned line-by-line. The data of a single k-space line are frequency-coded by means of a gradient upon readout. Each line in k-space has the interval Δky that is generated by a phase coding step. Since the phase coding requires a large amount of time in comparison to other spatial codings, most methods (for example the aforementioned “partially parallel acquisition”, designated in the following as PPA) are based on a reduction of the number of time-consuming phase coding steps to shorten the image measurement time. The fundamental idea in PPA imaging is that the k-space data are acquired not by a single coil but (according to FIG. 3A) by a (for example linear) arrangement of component coils (coil 1 through coil 3)—a coil array. Each of the spatially independent coils of the array has certain spatial information associated therewith that is used in order to achieve a complete spatial coding via a combination of the simultaneously acquired coil data. This means that multiple different displaced lines 32 (represented in following figures by dots) can also be determined (i.e. reconstructed) from a single acquired k-space line 31 (shown in grey in following figures). Such completed, reconstructed data sets are shown in FIG. 3B for the case of three component coils.
The PPA methods thus use spatial information that are contained in the components of a coil arrangement in order to partially replace the time-consuming phase coding that is normally generated using a phase coding gradient. The image measurement time is thereby reduced corresponding to the ratio of the number of lines of the reduced data set to the number of lines of the conventional (thus complete) data set. In a typical PPA acquisition, only a fraction (½. ⅓, ¼ etc.) of the phase coding lines are acquired in comparison to the conventional acquisition. A special reconstruction is then applied to the data in order to reconstruct the missing k-space lines, and therefore to obtain the full field of view (FOV) image in a fraction of the time.
The respective reconstruction method (which normally represents an algebraic method) corresponds to the respective PPA technique. The best known PPA techniques are image space-based methods such as SENSE (sensitivity encoding) and k-space-based methods such as GRAPPA (Generalized Autocalibration PPA) with their respective derivatives.
Additional calibration data points (additionally measured reference lines, for example 33 in FIG. 3) that are added to the actual measurement data and only on the basis of which a reduced data set can be completed again at all are not necessarily also acquired in all PPA methods.
In order to optimize the quality of the reconstruction and the SNR, a reconstruction according to GRAPPA—for example from a number N of incompletely measured data sets (except for the reference lines 33 of under-sampled coil images; FIG. 2: coil 1 to coil N)—again generates a number N of data sets (coil images) that—still in k-space—are respectively internally complete again. A Fourier transformation of the individual coil images thus leads to N aliasing-free single coil images whose combination in three-dimensional space (for example by means of sum-of-squares reconstruction) leads to an image optimized with regard to SNR and signal obliteration, however with the disadvantage that the calculation time for the GRAPPA image reconstruction is extremely increased given a high coil count.
The GRAPPA reconstruction (FIG. 2)—that, given N component coils, again leads to N complete single coil data sets—is based on a linear combination of the measured lines of an incomplete data set, wherein the determination of the (linear) coefficients necessary for this occurs in advance. For this it is sought to linearly combine the regular measured (thus the non-omitted) lines of an incomplete data set so that the additional measured reference lines (thus the calibration data points) are fitted to them with best possible fit. The reference lines thus serve as target functions that can be better adapted the more regular measured lines (possibly distributed among incomplete data sets of different component coils) that are present.
This means that, in the context of a GRAPPA reconstruction, the incomplete data sets of N component coils must be mapped to the N component coils again to complete these data sets. In this context, one also speaks of N GRAPPA input channels that are mapped to N GRAPPA output channels. This “mapping” ensues algebraically through a vector matrix multiplication, wherein the vectors represent the regular measured k-space lines and the matrix represents the determined GRAPPA coefficient matrix. In other words, this means that: if a linear combination of measured lines on the basis of a coefficient matrix yields a good approximately to the reference lines (calibration data points), omitted (and therefore not measured) lines of equal rank can be reconstructed just as well with this matrix. The coefficients are often also designated as weighting factors; the reference lines carry information about the coil sensitivities.
It can now be shown that the calculation time for the entire reconstruction method according to GRAPPA (i.e. for the determination of the GRAPPA coefficient matrix as well as for the mapping itself) possesses a quadratic (in some cases even a “super-quadratic”) dependency on the coil count N, which is not of any significant consequence given a lower coil count (8 channels<<1 minute) but given a higher coil count (N≧32) leads to unacceptable calculation times with regard to computing capacity and memory capacity of the system computer.
In order to cope with the increasing requirements with regard to CPU load and computer memory in PPA imaging, the conventional approach has been to use more powerful computers with more access memory and main memory (RAM) as well as multiprocessor-based parallel computers that can execute the PPA reconstruction algorithms in parallel, but that inherently represent an immense cost factor.
A GRAPPA-like method is also known from DE 10 2005 018 814 B4 that accelerates the image reconstruction method in GRAPPA insofar as that the computer time is kept within presently tolerable limits, even given high coil count. This is achieved by no longer reconstructing all unmeasured k-space lines of each coil, and instead reconstructing only a subset (for example only every third line of each coil), which corresponds to the operation in what is known as the P-mode or primary mode of a hard-wired or software-based mode matrix configuration of the MRT apparatus. A slight reduction of the output channels already reduces the complexity of the GRAPPA reconstruction matrix such that the required computer time for GRAPPA reconstruction is significantly reduced. However, because all N (see FIG. 5A) incompletely measured data sets are no longer completed and Fourier-transformed by GRAPPA reconstruction, rather only a subset of the N incompletely measured data sets, and this reduced set of incomplete data sets is now completed, Fourier-transformed and superimposed by GRAPPA reconstruction (see FIG. 5B), this means that reconstructable information (the omitted k-space lines) is potentially discarded. This entails a certain degradation of the signal-to-noise ratio that must presently be accepted with reduction of the calculation time.